Question

A set of angles has a ratio of 5 to 2. If the larger angle measures 105 degrees then what is the measure of the smaller angle

Answer 1

Answer: 42° is the measure of the smaller angle.

Explanation:

Since, the ratio of larger and smaller angle= 5:2

let larger angle= 5x and smaller=2x , where x is any number.

According to the question, larger angle = 105°

So, 5x=105° ⇒x=105°/5=21°

Thus, smaller angle = 2x= 2×21°=42°

Answer 2

If the larger angle measures 105 degrees, then the measure of the smaller angle is 42 degrees.

• Let the larger angle be L.

• Let the smaller angle be S.

Given the following data:

• Larger angle = 105 degrees

• Ratio of L to S = 5:2

• Total ratio= 5 + 2 = 7

To find the measure of the smaller angle, we would use direct proportion:

5 = 2

105 = X

Cross-multiplying, we have:

$5x = 2$ × $105$

$5x = 210\\\\x = \frac{210}{5}$

x = 42 degrees.

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